Electron density maps corresponding to macromolecules such as proteins have features that are different in fundamental ways from features found in maps calculated with random phases. These differences have been used in many ways, ranging from improving the accuracy of crystallographic phases to evaluating the quality of electron density maps (“maps” herein). For example, maps corresponding to proteins often have large regions of relatively featureless solvent, and large regions containing polypeptide chains, while a map calculated with random phases has similar fluctuations in density everywhere (Bricogne, 1974). This observation is the basis of the powerful solvent flattening approach (Bricogne, 1974; Wang, 1985) as well as methods for evaluating the quality of macromolecular electron density maps (e.g., Terwilliger et al., 1999). Similarly, the presence of non-crystallographic symmetry in macromolecular electron density maps has been useful in phase improvement (Bricogne, 1974, Rossmann, 1972; Kleywegt et al., 1998). Additionally, maps corresponding to macromolecules can be interpreted in terms of atomic models, providing a powerful basis for map quality evaluation and improvement (Agarwal et al., 1977; Lunin et al., 1984; Lamzin et al., 1993; Perrakis et al, 1997, 1999, 2001; Morris et al., 2002). On a statistical level, the density in the protein region of a macromolecular electron density map has a distribution that is very different than that in a map calculated with random phases. This has been extensively used in histogram-matching and related methods for phase improvement (Harrison, 1988; Lunin, 1988; Zhang et al., 1990; Zhang et al., 1997; Goldstein et al., 1998; Nieh et al., 1999; Cowtan, 1999).
The process of the present invention considers local patterns of density that are common in macromolecular protein structures. Macromolecules are built from small, regular, repeated units, and the packing of these units is highly constrained due to van der Waals interactions. Due to the regularity of macromolecules on a local scale, their electron density maps have local features that are distinctive and very different from those of maps calculated from random phases (Lunin, 2000; Urzhumtsev et al., 2000; Main et al., 2000; Wilson et al., 2000; Colovos et al., 2000). This property has been used to evaluate the quality of electron density maps and to improve phases at low resolution. For example, Lunin, 2000, Urzhumtsev et al., 2000, Main et al., 2000, and Wilson et al., 2000, use histogram and wavelet analysis to improve electron density in low-resolution maps by requiring the wavelet coefficients to be similar to those of model structures. Colovos et al., 2000, analyze the local features of high- and medium-resolution electron density maps and compare those features to corresponding features in model maps to evaluate the quality of the maps and suggest that their approaches may be useful for phase improvement as well.
A recent method for density modification consists of the identification of the locations of helical or other highly regular features in an electron density map, followed by statistical density modification using an idealized version of this density as the “expected” electron density nearby (Terwilliger, 2001). This method was shown to yield some phase improvement, but has the disadvantage that, after an initial cycle, the features that were initially identified became greatly accentuated, and few new features could be found. This effect may arise from the inherent feedback in the method, where a feature in the original electron density that partially matches a helical template is restrained to look like this template, making it an even better match for the template on the next round (even if the true density in the region is not helical).
The present invention uses the information inherent in local features of an electron density map that does not have this feedback to provide a capability for improvement in the features of the resulting electron density map, with concomitant improvement in the experimental phase information. The local patterns of density surrounding any point in a map have been found to be useful to estimate the electron density at that point. This observation makes it possible to begin with an electron density map with errors, to obtain a new estimate of the density at each point in the map without using the density at that point, and thereby to construct a new estimate of electron density with errors that are nearly uncorrelated with the errors in the original map. This recovered “image” of the electron density has many uses, including phase improvement and evaluation of map quality.
Various objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.